Two approaches have been applied to control designs based on this methodology: Lagrangian and Euler-Newtonian approach. In the Lagrangian approach, by exploring the physic properties of a Lagrangian system, i.e., the energy conservation characterized by the positiveness of the mass/inertial matrix and the skew-symmetry of some matrices involved in the Lagrangian dynamics, it enables proposing energy-like Lyapunov function candidates. The resulting controller consists of a PD action obtained as the gradient of the potential energy and the kinetic energy of closed loop plus some form of feedforward compensation [1]}, [2]}, [3]}, [4]}, [5]}, [6]}. Up to date a broad class of tracking control designs has been proposed in the literature and can be readily applied to problems of controller development ranging from basic full-state (position and velocity) feedback [7]}, output (position) feedback [4]}, adaptive [9]}, [10]}, [11]}, [12]}, and robust compensations of uncertainties/external disturbances [13]}, [14]}, [15]}, to decentralized control [16]}, [17]}, [18]} and coordination among a set of Lagrangian systems [19]}, [20]}, [21]}.
